Stochastic Frontier Analysis (SFA)

Stochastic frontier analysis (SFA) is a parametric method that estimates a production or cost frontier while splitting deviations from it into random noise and one-sided inefficiency.

확률변경분석(SFA)은 생산 또는 비용 변경(프런티어)을 추정하면서 변경으로부터의 편차를 무작위 오차와 한쪽 방향의 비효율로 분리하는 모수적 방법이다.

How do I measure the efficiency of firms or units while allowing for random noise?

무작위 오차를 고려하면서 기업이나 단위의 효율성을 어떻게 측정하나요?

Stochastic frontier analysis estimates the maximum output, or minimum cost, achievable from given inputs and separates each unit's shortfall into random noise and inefficiency. It fits efficiency studies of firms, hospitals or farms where a functional form such as Cobb-Douglas or translog is reasonable.

When to use Stochastic Frontier Analysis (SFA)

• An output or cost measure with input quantities or prices for many units
• Separating inefficiency from measurement error and random shocks
• Explaining inefficiency with unit characteristics

When to use something else

• No functional form can be justified or multiple outputs without prices; use data envelopment analysis
• Interest is only in average relationships; use ordinary least squares regression

Assumptions and requirements

• Correct functional form of the frontier
• Distributional assumption for inefficiency (half-normal, truncated normal or exponential)
• Symmetric noise term independent of inefficiency
• Inputs not strongly endogenous

What the analysis reports

• Frontier coefficients and elasticities
• Variance parameters (sigma-squared, lambda or gamma)
• Likelihood ratio test for presence of inefficiency
• Unit-level technical efficiency scores

How to report it

The stochastic frontier model indicated significant inefficiency (γ = [value], p = [value]), and mean technical efficiency was [value].

Related methods

• Data Envelopment Analysis
• Cobb-Douglas Production Function
• Tobit Regression

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